The displacement u ( t ) of the mass from it’s equilibrium position satisfies the differential equation m u ″ + γ u ′ + k u + ε u 3 = 0 .

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Answer 1

Question

Chapter 3.7, Problem 24P

a.

To determine

To show: The displacement u(t) of the mass from it’s equilibrium position satisfies the differential equation mu″+γu′+ku+εu3=0.

b.

To determine

The displacement u(t) when ε=0 and hence obtain the amplitude and period of the motion.

c.

To determine

To graph: The numerical approximation of the solution when ε=0.1 and hence estimate the amplitude and period.

d.

To determine

To graph: The numerical approximation of the solution when ε=0.2 and ε=0.3 and hence estimate the amplitude and period.

e.

To determine

To graph: The estimated values of the amplitude and the period versus ε and hence describe how it depends on ε.

f.

To determine

To graph: The numerical approximation of the solution when ε=−0.1, ε=−0.2 and ε=−0.3, estimate the amplitude and period and hence plot the estimated values of the amplitude and the period versus ε and describe how it depends on ε.

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Answer 2

Question

Chapter 3.7, Problem 24P

a.

To determine

To show: The displacement u(t) of the mass from it’s equilibrium position satisfies the differential equation mu″+γu′+ku+εu3=0.

b.

To determine

The displacement u(t) when ε=0 and hence obtain the amplitude and period of the motion.

c.

To determine

To graph: The numerical approximation of the solution when ε=0.1 and hence estimate the amplitude and period.

d.

To determine

To graph: The numerical approximation of the solution when ε=0.2 and ε=0.3 and hence estimate the amplitude and period.

e.

To determine

To graph: The estimated values of the amplitude and the period versus ε and hence describe how it depends on ε.

f.

To determine

To graph: The numerical approximation of the solution when ε=−0.1, ε=−0.2 and ε=−0.3, estimate the amplitude and period and hence plot the estimated values of the amplitude and the period versus ε and describe how it depends on ε.

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Answer 3

Question

Chapter 3.7, Problem 24P

a.

To determine

To show: The displacement u(t) of the mass from it’s equilibrium position satisfies the differential equation mu″+γu′+ku+εu3=0.

b.

To determine

The displacement u(t) when ε=0 and hence obtain the amplitude and period of the motion.

c.

To determine

To graph: The numerical approximation of the solution when ε=0.1 and hence estimate the amplitude and period.

d.

To determine

To graph: The numerical approximation of the solution when ε=0.2 and ε=0.3 and hence estimate the amplitude and period.

e.

To determine

To graph: The estimated values of the amplitude and the period versus ε and hence describe how it depends on ε.

f.

To determine

To graph: The numerical approximation of the solution when ε=−0.1, ε=−0.2 and ε=−0.3, estimate the amplitude and period and hence plot the estimated values of the amplitude and the period versus ε and describe how it depends on ε.

Expert Solution & Answer

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Answer 4

Question

Chapter 3.7, Problem 24P

a.

To determine

To show: The displacement u(t) of the mass from it’s equilibrium position satisfies the differential equation mu″+γu′+ku+εu3=0.

b.

To determine

The displacement u(t) when ε=0 and hence obtain the amplitude and period of the motion.

c.

To determine

To graph: The numerical approximation of the solution when ε=0.1 and hence estimate the amplitude and period.

d.

To determine

To graph: The numerical approximation of the solution when ε=0.2 and ε=0.3 and hence estimate the amplitude and period.

e.

To determine

To graph: The estimated values of the amplitude and the period versus ε and hence describe how it depends on ε.

f.

To determine

To graph: The numerical approximation of the solution when ε=−0.1, ε=−0.2 and ε=−0.3, estimate the amplitude and period and hence plot the estimated values of the amplitude and the period versus ε and describe how it depends on ε.

Expert Solution & Answer

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Answer 5

Chapter 3.7, Problem 24P

a.

To determine

To show: The displacement u(t) of the mass from it’s equilibrium position satisfies the differential equation mu″+γu′+ku+εu3=0.

b.

To determine

The displacement u(t) when ε=0 and hence obtain the amplitude and period of the motion.

c.

To determine

To graph: The numerical approximation of the solution when ε=0.1 and hence estimate the amplitude and period.

d.

To determine

To graph: The numerical approximation of the solution when ε=0.2 and ε=0.3 and hence estimate the amplitude and period.

e.

To determine

To graph: The estimated values of the amplitude and the period versus ε and hence describe how it depends on ε.

f.

To determine

To graph: The numerical approximation of the solution when ε=−0.1, ε=−0.2 and ε=−0.3, estimate the amplitude and period and hence plot the estimated values of the amplitude and the period versus ε and describe how it depends on ε.

Answer 6

Chapter 3.7, Problem 24P

a.

To determine

To show: The displacement u(t) of the mass from it’s equilibrium position satisfies the differential equation mu″+γu′+ku+εu3=0.

Answer 7

Chapter 3.7, Problem 24P

a.

To determine

To show: The displacement u(t) of the mass from it’s equilibrium position satisfies the differential equation mu″+γu′+ku+εu3=0.

Answer 8

b.

To determine

The displacement u(t) when ε=0 and hence obtain the amplitude and period of the motion.

Answer 9

b.

To determine

The displacement u(t) when ε=0 and hence obtain the amplitude and period of the motion.

Answer 10

c.

To determine

To graph: The numerical approximation of the solution when ε=0.1 and hence estimate the amplitude and period.

Answer 11

c.

To determine

To graph: The numerical approximation of the solution when ε=0.1 and hence estimate the amplitude and period.

Answer 12

d.

To determine

To graph: The numerical approximation of the solution when ε=0.2 and ε=0.3 and hence estimate the amplitude and period.

Answer 13

d.

To determine

To graph: The numerical approximation of the solution when ε=0.2 and ε=0.3 and hence estimate the amplitude and period.

Answer 14

e.

To determine

To graph: The estimated values of the amplitude and the period versus ε and hence describe how it depends on ε.

Answer 15

e.

To determine

To graph: The estimated values of the amplitude and the period versus ε and hence describe how it depends on ε.

Answer 16

f.

To determine

To graph: The numerical approximation of the solution when ε=−0.1, ε=−0.2 and ε=−0.3, estimate the amplitude and period and hence plot the estimated values of the amplitude and the period versus ε and describe how it depends on ε.

Answer 17

f.

To determine

To graph: The numerical approximation of the solution when ε=−0.1, ε=−0.2 and ε=−0.3, estimate the amplitude and period and hence plot the estimated values of the amplitude and the period versus ε and describe how it depends on ε.

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

Ch. 3.1 - Prob. 1P Ch. 3.1 - Prob. 2P Ch. 3.1 - Prob. 3P Ch. 3.1 - Prob. 4P Ch. 3.1 - Prob. 5P Ch. 3.1 - Prob. 6P Ch. 3.1 - Prob. 7P Ch. 3.1 - Prob. 8P Ch. 3.1 - Prob. 9P Ch. 3.1 - Prob. 10P

The displacement u ( t ) of the mass from it’s equilibrium position satisfies the differential equation m u ″ + γ u ′ + k u + ε u 3 = 0 .

To show: The displacement u(t) of the mass from it’s equilibrium position satisfies the differential equation mu″+γu′+ku+εu3=0.

The displacement u(t) when ε=0 and hence obtain the amplitude and period of the motion.

To graph: The numerical approximation of the solution when ε=0.1 and hence estimate the amplitude and period.

To graph: The numerical approximation of the solution when ε=0.2 and ε=0.3 and hence estimate the amplitude and period.

To graph: The estimated values of the amplitude and the period versus ε and hence describe how it depends on ε.

To graph: The numerical approximation of the solution when ε=−0.1, ε=−0.2 and ε=−0.3, estimate the amplitude and period and hence plot the estimated values of the amplitude and the period versus ε and describe how it depends on ε.

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Chapter 3 Solutions